Questions:
COURSE: BSC (IT)
SUBJECT: COMPUTER ORIENTED NUMERICAL ANALYSIS
ASSIGN MENTA
(Any three)
 Solve the following set of equation by Gauss elimination method.
2x +3y+4z=12
3x + y +z=4
x+4y+z=5
SOLUTION –
 Find the rate of convergence of Newton Raphson method. Solve by www.solvezone.in
Solution
 Define error, relative error and absolute error, give example of each.
Solution
ASSIGNMENTB
 a) Round off and truncate the following numbers to the four decimal places.
 a) 132.5983
 b) 0.073729
Solution 
 Solve the following equation by Jacobi method. Perform three steps.
x₁2x₂x₃x₄=3
2x₁ + x₂x₃ x₄=15
x₁ – x₂ + x₃ 2x₄ =27
x₁ x₂2x₃+x₄ =9
Solution –
 For a given data
X

F(x)

1

33

2

50

3

69

4

90

5

129

Find the value of f(x) at 1.4
Solution
ASSIGNMENT C
 The order of convergence of NewtonRaphson method is
(A): 2
(B): 3
(C): 0
(D): 1
 One of the roots of the equation x33x2+x3=0 is
(A): 1
(B): 1
(C): √3
(D): 3
 The solution to the set of equations:
25x+y+z=25; 64x+8y+z=71; 114x+12y+z=155
The most nearly value of ??,??,??=
(A): (1,1,1)
(B): (1,1,1)
(C): (1,1,1)
(D): Does not have a unique solution
 The order of convergence of Regulafalsi method is
(A): 1.235
(B): 3.141
(C): 1.618
(D): 2.792
 Newton’s iterative formula to find the value of √N is
Ans. D
 The NewtonRaphson method fails when
Ans. D
 The one of the root of the equation x^34x9=0 using bisection method is
(A): 2.5065
(B): 2.6066
(C): 2.7066
(D): 3.5066
 Which of the following is increasing order of convergence method for finding roots
(A): Bisection, regulafalsi, newton Raphson
(B): Regulafalsi, Bisection, Newton Raphson
(C): Newton Raphson, Regula falsi, bisection
(D): Bisection, Newton Raphson, regulafalsi
 If X is a true value and X is its approximate value then absolute error ea is
Ans A
 If X is a true value and X is its approximate value then Relative error er is
Ans. D
 Any quadratic equation f(x)=0 has
(A): One root
(B): Two roots
(C): Three roots
(D): Four roots
 An equation such as tanx=x has
(A): Zero roots
(B): One root
(C): Two roots
(D): Infinite roots
 The roots of an equation f(x)=x^3x1=0 lies between
(A): f(2) and f(3)
(B): f(3) and f(4)
(C): f(1) and f(2)
(D): All of these
 The real roots of an equation f(x)=xex2=0 using newton Raphson method is
(A): 0.5682
(B): 0.8526
(C): 0.3525
(D): 1.5000
 Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The process of finding the value of y corresponding to any value of x (between x_0 and x_n) is called
(A): Extrapolation
(B): Interpolation
(C): Differentiation
(D): Integration
 Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The process of finding the value of y corresponding to any value of x (outside of the range x_0 and x_n) is called
(A): Extrapolation
(B): Interpolation
(C): Differentiation
(D): Integration
 Given n+1 data pairs (x_0,y_0),(x_1,y_1),… (x_n,y_n). The n^(th ) forward difference is
(A): ?n yr=?(n1) y(r+1)?(n1) yr
(B): ?n yr=?(n1) y(r+1)?(n1) yr
(C): ?^n y_r=?^n y_(r+1)?^n y_r
(D): ?^n y_r=?^n y_r?^(n1) y_(r1)
 If ? is forward difference operator and E is a shift operator then
(A): ?=E1
(B): ?=E+1
(C): E=?1
(D): None of these
 If δ is central difference operator and E is a shift operator then
Ans. D
 The rate of convergence of Bisection method for finding roots is
(A): 2
(B): 3
(C): 1.5
(D): 1.0
 A second degree polynomial passes through (0,1),(1,3), (2,7), (3,13), then the polynomial f(x) is
Ans C
 Given data pairs (1,7),(2,x),(3,13),(4,21),(5,37). The value of x is
(A): 10.5
(B): 9.5
(C): 12.5
(D): 12.0
 Which of the following Interpolation formula is used for unequally spaced points
(A): Newton forward
(B): Newton backward
(C): Lagrange formula
(D): Euler formula
 1)=1, P(3)=27, P(4)=64, Using Lagrange interpolation formula, the polynomial P(x) of degree 2 is:
Ans. D
 Putting n=1 in the newtonCote’s quadrature formula, we have
(A): Trapezoidal rule
(B): Simpson’s 1/3 formula
(C): Simpson’s 3/8 formula
(D): Euler’s formula
 Putting n=3 in the newtonCote’s quadrature formula, we have
(A): Trapezoidal rule
(B): Simpson’s 1/3 formula
(C): Simpson’s 3/8 formula
(D): Euler’s formula
 Which of the following method required odd number of points for integration
(A): Trapezoidal rule
(B): Simpson’s formula
(C): Both Trapezoidal & Simpson
(D): None of these
 Using Trapezoidal rule, the value of
(A): 1.3662
(B): 1.4107
(C): 1.3570
(D): 1.5706
 Which of the following symbol is called backward difference operator
(A): ?
(B): ∇
(C): δ
(D): E
 Newton divided difference method for interpolation can be used for
(A): Equal spaced points
(B): Unequal spaced points
(C): Not well defined
(D): All of these
 Which of the following is NOT a method to solve ordinary differential equation
(A): Euler’s method
(B): Picard’s method
(C): Taylor series method
(D): Romberg’s method
 Euler’s formula for solving ordinary differential equation is
Ans. D
 Which of the following is a Runga kutta 2nd order formula
Ans. C
 Taylor series method is used for
(A): Integration
(B): Differentiation
(C): Ordinary differential equation
(D): Roots finding
 Polynomials are most commonly used functions for interpolation because they are easy to
(A): Evaluate
(B): Differentiate
(C): Integrate
(D): Evaluate, differentiate, and integrate
 To solve the ordinary differential equation using Runga kutta 2nd order, we need to write the equation
Ans. D
 Picard’s method is used to solve
(A): Integration
(B): Differentiation
(C): Ordinary Differential equation
(D): Roots finding
 The inverse of a matrix A is written as
(A): Identity matrix
(B): Null matrix
(C): Singular matrix
(D): Inverse matrix
 he second forward difference

Ans. D